Respuesta :

GoddessofDork
  • i = [tex] \sqrt{-1} [/tex]
  • Product rule of radicals: √ab = √a x √b

Firstly, factor out i: [tex] i\sqrt{50} [/tex]

Next, apply the product rule of radicals here as such:

[tex] i\sqrt{50}=i\sqrt{10\times 5}=i\sqrt{5\times 2\times 5}=5i\sqrt{2} [/tex]

Your answer is 5i√2, or the second option.

just to add to @GoddessofDork superb reply above.


[tex] \bf \sqrt{-50}\implies \sqrt{-1\cdot 50}\implies \sqrt{-1}\cdot \sqrt{50}~~
\begin{cases}
50=2\cdot 5\cdot 5\\
\qquad 2\cdot 5^2
\end{cases}\implies \sqrt{-1}\cdot \sqrt{2\cdot 5^2}
\\\\\\
i\cdot 5\sqrt{2}\implies 5i\sqrt{2} [/tex]

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